Unveiling climate complexity: a multifractal approach to drought, temperature, and precipitation analysis

Multifractal analysis has become a crucial methodology for understanding terrestrial phenomena, offering unique insights into chaotic systems with multi-scale variability. Originally from statistical physics, this approach is valuable for studying geophysical events such as droughts, temperature fluctuations, and rainfall impacts on water resources. Multifractals effectively characterize the scaling behaviors necessary to analyze irregular and nonlinear dynamics in these processes. This paper highlights prominent multifractal techniques, including Multifractal Detrended Fluctuation Analysis (MF-DFA), Generalized Structure Functions (GSF), Multifractal Height Cross-Correlation Analysis (MF-HXA), Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), Multifractal Detrending Moving-Average Cross-Correlation Analysis (MFXDMA), Multifractal Cross-Correlation Analysis Based on Statistical Moments (MFSMXA), Multifractal Inverse Distance Weighting (MIDW), and wavelet-based methods (WBM). These approaches capture both minor and major fluctuations within geophysical data, providing a more nuanced representation than conventional statistical methods. By transcending traditional statistics, multifractal analysis enhances predictive modeling for extreme weather events, like prolonged droughts and unusual precipitation patterns, anticipated to increase in frequency and intensity with climate change. This article reviews multifractal methodologies, their contributions to climate science, and potential future research directions, focusing on drought, temperature, and precipitation. Additionally, it bridges complex theoretical frameworks with practical applications, underscoring the significance of multifractal models in advancing climate research.